Vivek is older than Kishor by 5 years. The Find their present ages is

1.	Vivek is older than Kishor by 5 years. The Find their present ages is 1/6 Find their Present ages
Answer» Let the present age of Kishor be x. ∴ Present age of Vivek = (x + 5) years According to the given condition, \(\frac{1}{x}\) + \(\frac{1}{x + 5}\) = \(\frac{1}{6}\) ∴ \(\frac{x+5+x}{x(x+5)}\) = \(\frac{1}{6}\) ∴ \(\frac{2x +5}{x(x+5)}\) = \(\frac{1}{6}\) ∴ 6(2x + 5) = x(x + 5) ∴ 12x + 30 = x² + 5x ∴ x² + 5x – 12x – 30 = 0 ∴ x² – 7x – 30 = 0 ∴ x² – 10x + 3x – 30 = 0 ∴ x(x – 10) + 3(x – 10) = 0 ∴ (x – 10)(x + 3) = 0 By using the property, if the product of two numbers is zero, then at least one of them is zero, we get ∴ x – 10 = 0 or x + 3 = 0 ∴ x = 10 or x = – 3 But, age cannot be negative ∴ x = 10 andx + 5 = 10 + 5 = 15 ∴ Present ages of Kishor and Vivek are 10 years and 15 years respectively.

Vivek is older than Kishor by 5 years. The Find their present ages is 1/6 Find their Present ages

Answer»

Let the present age of Kishor be x.

∴ Present age of Vivek = (x + 5) years According to the given condition,

\(\frac{1}{x}\) + \(\frac{1}{x + 5}\) = \(\frac{1}{6}\)

∴ \(\frac{x+5+x}{x(x+5)}\) = \(\frac{1}{6}\)

∴ \(\frac{2x +5}{x(x+5)}\) = \(\frac{1}{6}\)

∴ 6(2x + 5) = x(x + 5)

∴ 12x + 30 = x² + 5x

∴ x² + 5x – 12x – 30 = 0

∴ x² – 7x – 30 = 0

∴ x² – 10x + 3x – 30 = 0

∴ x(x – 10) + 3(x – 10) = 0

∴ (x – 10)(x + 3) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

∴ x – 10 = 0 or x + 3 = 0

∴ x = 10 or x = – 3

But, age cannot be negative

∴ x = 10 andx + 5 = 10 + 5 = 15

∴ Present ages of Kishor and Vivek are 10 years and 15 years respectively.